T1W8L3

basic cubic function §

• the basic cubic function is $y=x^3$
  • key features of the functions is that
  • horizontal inflection point at the origin $(0,0)$
  • intercepts: both at $(0,0)$
  • end behaviour:
    • as $x\to \infty ,y\to \infty$
    • as $x\to -\infty ,y\to -\infty$

features of f(x) = a(x-h)^3 + k §

• to graph, transform y=x^3 as follows:

1. dilate by a factor of |a| from the x-axis - or along the y-axis

   feature	value or location
   horizontal inflection point	(h,k)
   end behaviour	when a>0: as $x\to \infty ,y\to \infty$ blah blah blah something else oops i didnt write it down in time check onennote

• find x-intercepts, blah blah, sketch it.